To solve this problem, we need to analyze the geometry in the circle provided.

1. We are given that $\angle OPQ = 35^\circ$.
2. $O$ is the center of the circle, and $\angle OPQ$ is an angle formed at point $P$, with $Q$ on the circle.
3. We are asked to find the measure of $\angle PRQ$, which is an inscribed angle that subtends the arc $PQ$.

Solution Steps

1. Since $\angle OPQ$ is given as $35^\circ$, we know that this is the angle at $P$ with respect to the center.
2. In a circle, an inscribed angle (like $\angle PRQ$) is half the measure of the central angle that subtends the same arc.
3. Therefore, $\angle PRQ = \frac{1}{2} \times \angle OPQ = \frac{1}{2} \times 35^\circ = 17.5^\circ$.

Answer

The measure of $\angle PRQ$ is $17.5^\circ$.

Would you like more details on the solution or have any questions?

Here are some related questions for further exploration:

1. How do you calculate the angle at the center if an inscribed angle is given?
2. What is the relationship between central and inscribed angles in a circle?
3. Can you explain why an inscribed angle is half the central angle in a circle?
4. How would the solution change if the circle was not centered at $O$?
5. What would happen to $\angle PRQ$ if $\angle OPQ$ was changed?

Tip: In circle geometry, remember that the measure of an inscribed angle is always half the central angle subtending the same arc.